I think rudy rucker uses this in his cubic connectedness map cubic mandelbrot formula. It has six parameter spaces. -david ----- Original Message ----- From: <fractint-request@mailman.xmission.com> To: <fractint@mailman.xmission.com> Sent: Saturday, April 17, 2004 6:27 AM Subject: Fractint Digest, Vol 14, Issue 7
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Today's Topics:
1. Re: FOTD 15-04-04 (Land of Fractals [5]) (SherLok Merfy) 2. Re: FOTD 15-04-04 (Land of Fractals [5]) (James R. McKenzie) 3. FOTD 16-04-04 (Image of Springtime [5]) (Jim Muth) 4. nntp:/news.admin.net-abuse.sightings (SherLok Merfy) 5. Re: FOTD 15-04-04 (Land of Fractals [5]) (Paul N. Lee) 6. Re: FOTD 16-04-04 (Image of Springtime [5]) (Paul N. Lee) 7. FOTD 17-04-04 (Polyester Minibrot [7]) (Jim Muth)
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Message: 1 Date: Thu, 15 Apr 2004 10:00:43 -0600 (MDT) From: SherLok Merfy <brewhaha@freenet.edmonton.ab.ca> Subject: Re: [Fractint] FOTD 15-04-04 (Land of Fractals [5]) To: Fractint and General Fractals Discussion <fractint@mailman.xmission.com> Cc: philofractal@lists.fractalus.com Message-ID: <Pine.A41.3.95.1040415094447.29258D-100000@freenet.edmonton.ab.ca> Content-Type: TEXT/PLAIN; charset=US-ASCII
On Thu, 15 Apr 2004, Jim Muth wrote: (...)
frm:OblateMix2 {; Jim Muth z=real(pixel)+flip(real(p3)), c=fn1(flip(imag(pixel)))+imag(p3), (...) Dynamic real, and static imajinary -- then vice-versa. Nobody has a monopoly on stuff that only they know how to work (or read, as the case may be), but even if the formula doesn't spred, that's an interesting idea.
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Message: 2 Date: Thu, 15 Apr 2004 14:56:51 -0400 From: "James R. McKenzie" <jimmckenzie@earthlink.net> Subject: Re: [Fractint] FOTD 15-04-04 (Land of Fractals [5]) To: "Fractint and General Fractals Discussion" <fractint@mailman.xmission.com> Message-ID: <000901c4231b$698d8cf0$09fb1743@yourxhtr8hvc4p> Content-Type: text/plain; charset="iso-8859-1"
This only rates a "5"? I wish I could run Fractint in XP (Been there tried that, no go) so I could do a 3D transform of the image and see what comes up or "out" as it were. 8-{>
BTW if anyone does a 1280x1024 of this e-mail me, I'd like a copy. ----- Original Message ----- From: "Jim Muth" <jamth@mindspring.com> To: <fractint@mailman.xmission.com> Cc: <philofractal@lists.fractalus.com> Sent: Thursday, April 15, 2004 10:52 AM Subject: [Fractint] FOTD 15-04-04 (Land of Fractals [5])
FOTD -- April 15, 2004 (Rating 5)
Fractal visionaries and enthusiasts:
Today's image takes us into the fourth dimension. I have always been fascinated by the fourth dimension. I was not yet a teen-ager when, having just finished a book, (I think its name was "One, Two, Three, Infinity..."), I asked my father where the fourth dimension is, and, thinking of relativity, he told me that it is in the past and the future. This was not a very satisfactory answer. The past and future are time, not space. I wanted to know where the fourth dimension of space is. He then explained to me that as far as we know, there is no fourth spatial dimension, and even if there were, we would perceive it in three-dimensional terms.
This is the problem. We are brain-washed to perceive our surroundings as a three-dimensional world. We have not been wired to perceive a four-dimensional space, and it is too late to change that. If we were suddenly dropped into a four- dimensional world, we would not see the fourth dimension. We would see a three-dimensional world that obeyed different rules. Solid objects would change shape as we watched; objects would appear and vanish. We would think the world had gone crazy. We would probably go crazy ourselves, (as some say I already have), but we would be no closer to visualizing the fourth dimension.
Even now, we are able to fully visualize and understand the shadows that would be cast by four-dimensional objects onto the three-dimensional surface of our space. A 4-D hypersphere would cast a spherical shadow if the ray of light fell perpendicularly onto our space. If the light struck our space at an angle, we would see an oblate spheroid, the eccentricity of which would vary with the angle of the ray of light. But even though we understand all of this, we are still totally unable to visualize the hypersphere that would be casting the shadow.
We can also know and fully visualize the three-dimensional slices of four-dimensional objects. The 4-D hypercube may be sliced to give many curious prisms, as well as a tetrahedron and an octahedron, and of course the expected cube. But even this is of no help in our quest to realize the fourth dimension.
Our lack of visualizing ability is curious. We can program our computers to 'think' in four dimensions almost as easily as in three. We could even give them three-dimensional screens on which to better display the 4-D worlds they would have no trouble in manipulating. Of course, we would then be unable to view the 3-D screens in the proper manner, from outside our space. We would of necessity need to view the screens 'edge-on'. We appear to be forever doomed, trapped in a world of three dimensions, while able to know of the far greater vistas that would lie before us if only we could rewire our minds.
Since our minds are not about to be rewired, it's best we turn to today's image.
Today's image is a two-dimensional slice of a four-dimensional object. In this case, the object is the 4-D Julibrot created by iterating the formula (1/Z)-Z+C. I have sliced the Julibrot in what I call the Oblate direction, which is determined by the imaginary C and real Z axes.
The picture has a certain surreal quality about it, which inspired the above outburst about higher dimensions. It could almost be something we might see if we were suddenly dropped into a four-dimensional space. This is why I named the picture "Land of Fractals".
Since the image is such a departure from my usual fractal fare, I was not sure how to rate it. I finally decided on a rating of an average 5. The short render time of 2-1/2 minutes raises the overall value to a mighty 202.
An alternate way of seeing the other-worldly scene is to download it from the FOTD web site at:
<http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
Light rain fell steadily all day Wednesday here at Fractal Central, keeping the fractal duo confined to the indoors. Even if it had not been raining, the temperature of 50F 10C would have been a bit chilly for their sensitive ears. Today is starting windy and chilly, but sunny. We'll see how the dynamic fractal cats take these conditions.
For me it's work before play. The problem comes in separating the two. Until tomorrow's FOTD, take care, and most likely it's fractals all the way down.
Jim Muth jamth@mindspring.com jimmuth@aol.com
START 20.0 PAR-FORMULA FILE================================
Land_of_Fractals { ; time=0:02:28.69--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=OblateMix2 function=ident passes=1 center-mag=-4.55271/3.10114/0.6584367/8.9718/-11.2\ 262659607652502/29.222244310548934 params=1/-1/-1/1/1/-0.2 float=y maxiter=1200 inside=255 logmap=yes periodicity=10 colors=000Di`Ei_FiZFhZGhYGhXHhWHhWHhWU_`fRfuHlsIkr\ JjpKjmLiUdkUckUbjUaiU`hU_gUZfUYeUXdUWcUWcUVbUVbUUa\ TUaST`QT`RS_PS_NRZMRZKQYJQYHPXGPXENWDLWBIVAGV8EU7C\ U8ET9MTANSBOSBPRCQRDRQETQFUPFWPGYOH_NIaMIcLJeKKgJL\ iIMkIMmINoIOqIPsINsHPtIQtIStITuJVuJWuJYvKZvK`vKawL\ cwLdwLfwLgxMixMjxMlyNmyNoyNpzOrzOszOtzOuvPusPupPum\ PvjPvgPvdPvaPubRtcTscVrdXqdZpe_oeanfcnfemgglgikhjj\ hliinhipgjrfhygjshlninhjpckrZltTmvOnxJozDpz8pz3lxE\ hrPdm_`gjYcvXbtXbsXbrXbqWbpWboWbnWbmVbkVbjVbiVbhUb\ gUbfUbeUbdUbcW`bY_bZZb`YbaWbcVbeUbfTbhRbiQbkPblObj\ NahNafM`dM`bL_`L_ZKZXKZVJYTJYRIXPIXNHWLHWJGVHGVFFU\ DFUBET9ET7DS5DS8GTBITELTGNTJQTMSTOVURXUU_UWaUZdUaf\ UgkVchU_fUXdTTbTQ`SMYSIWRFURBSQ2UJ8QQEMWKIbQEjPFhP\ GgPHfPIeOJdOKbOLaOL`NM_NNZNOYNPWNQVMRUMRTMSSMTQLUP\ LVOLWNLXMHUMLXLP_KTbJXeJ_gIcjHgmHkpGosFstCruFrvIrw\ LqxNqyQqzTqzWpzYpz`pzccwz }
frm:OblateMix2 {; Jim Muth z=real(pixel)+flip(real(p3)), c=fn1(flip(imag(pixel)))+imag(p3), a=real(p1), b=imag(p1), d=real(p2), f=imag(p2): z=(a*(z^b))+(d*(z^f))+c, |z| <= 100 }
END 20.0 PAR-FORMULA FILE==================================
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Message: 3 Date: Fri, 16 Apr 2004 10:45:46 -0400 From: Jim Muth <jamth@mindspring.com> Subject: [Fractint] FOTD 16-04-04 (Image of Springtime [5]) To: fractint@mailman.xmission.com Message-ID: <1.5.4.16.20040416104907.0d67ef6e@pop.mindspring.com> Content-Type: text/plain; charset="us-ascii"
FOTD -- April 16, 2004 (Rating 5)
Fractal visionaries and enthusiasts:
A longer version of today's discussion appears on the philofractal list.
Today's image, which combines various unlikely negative portions of Z^(-1.4) and Z^(-14), has a certain feeling of springtime to it. Since the season here in the Northern Hemisphere is in fact spring, I named the picture "Image of Springtime".
The shades of pink and white could be apple or cherry blossoms. The greens could be the newly emerged leaves. The blues, of course, are nothing but the blue of a clear springtime sky.
It's a relatively harmless image, not stressful to look at, one that I have rated a 5. The render time of under 4 minutes raises the overall value to 135. The finished product is available on the FOTD web site at:
<http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
Thursday was a good day here at Fractal Central. Warm sun, cloudless skies, moderate winds and a temperature of 63F 17C gave the dynamic duo a very pleasant afternoon in the yard. When evening arrived, they came inside without urging. Today promises to be even warmer. I expect another good day.
The work is moderate today. Hopefully, the next fractal will be of above moderate quality . Until next time, take care, and the fractals never end.
Jim Muth jamth@mindspring.com jimmuth@aol.com
START 20.0 PAR-FORMULA FILE================================
Image_ofSpringtime { ; time=0:03:42.48--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=mandelbrotmix4 function=recip passes=1 center-mag=+1.46839349750336400/+0.281643707741821\ 60/9.037591e+009/1/-19.9987125907157584/-0.0014716\ 5417249400798 params=-4.5/-1.4/-0.9/-14/0/0 float=y maxiter=550 inside=0 outside=tdis periodicity=10 colors=000jKKhKKfKKdKKgMRkCTnBV1_X0ZZ0Z`0ZbLfhzvsz\ vsyqoymlyiiyefy`byX_yTXyPUyLRwJTuIVsGXqFZoE_kCvnBl\ i9hg8fe7hc5ja4l`3mb2Zc1Kd15c58c9BcDDcHGcLIcPLcTOcX\ Qc`TcdVchYcl_dlXelUflSflPglNhlKplHwlFjlCjlAkmHlmNk\ hPkcQkZSkUTkPVjKWjFYjAZj5`j1al4_m6Zo9YpBXrDWsGUuIT\ vKSxNRyPQzRPvTQrVQoXRkZRh_RdaSacSYeTVgTRhTOjUKlUHn\ VDpVAqVDpTFoRHnPJmNMlLOkKQjISiGVhEXgCZfA`e9XbHU_PR\ XXOUdLRkPPhSNeVLbYJ_`HXdFUgDRjBOm9Lp7IqCIrGIrKIsOI\ tSItWIu_IucInZHhUGbPFWKEQFDKBCQIIWPOaWUgb_miespjnn\ jjmjeljajjXijThjX_d_R_cIUfBPaGSXLVTPXOU_JZbFbdNd`U\ eXagThhPoiMlcGiYBfS6dM1YN6SOBMPGFQL9RQ3RUYh0kQMy8g\ vCesGdpKbnNakR`hVZeZYcaXFS0wk5phDjeKdbRZ`YSYeMVlGS\ sAQzBOwCMtDKrEIoFGlGEjHCgHAeEIhCQk9Yn7dpAcqCcrEcsH\ btJbuLbuM_mNYfOW_PUTQRMRPFSN8TL1XL7`LCcLHWONPRTHUZ\ SqcSqcJ`bOcbSeaWg`KMKKOMKQOMSQ0UN3WM6YK9_ICaHFcFIe\ DLgCNiOOkXQm`RocNqf5si4ul }
frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l }
END 20.0 PAR-FORMULA FILE==================================
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Message: 4 Date: Fri, 16 Apr 2004 10:01:45 -0600 (MDT) From: SherLok Merfy <brewhaha@freenet.edmonton.ab.ca> Subject: [Fractint] nntp:/news.admin.net-abuse.sightings To: Fractint and General Fractals Discussion <fractint@mailman.xmission.com> Cc: philofractal@lists.fractalus.com Message-ID: <Pine.A41.3.95.1040416091435.45044C-100000@freenet.edmonton.ab.ca> Content-Type: TEXT/PLAIN; charset=US-ASCII
(...)
Jim Muth wrote:
(248 junkers arrived since 11:30pm last evening.) .........maybe I'll (...) On Sun, 11 Apr 2004, Paul N. Lee wrote of Earthlink's spam blocker: In that way you will never have to download the junk-email at all.
You must know that the filters aren't that reliable. They begin with a bunch of sites that are basically avowed spammers. My address is about as old as Jim's, I post on USENET without a munged address, and yet my spam load is about a fifth.
The source of the difference is that my posts to nanas [NG shorthand] are declining in favour of carefully looking at the headers for the offender's site and notifying the postmaster at that site (forwarding complete headers). (Some people would tell you that abuse@ that site is the person to tell, but I don't think it makes a lot of difference).
No better way is to get on the more important cut-lists, than to let a spammer know that you report and that your reports get contracts cancelled (especially if they're not alone).
...which reminds me of imagelinkusa.net They seem to hav a Master Of Business Administration at their helpdesk, so I should check out the Mail Abuse Prevention System to see if they're already listed, and if they are then see if MY helpdesk has any idea how we might use the real-time black-hole list.
The discussion group in the hierarchy is news:/news.admin.net-abuse.email
I'm dead set against letting spammers chase ME around. If I get tired of it, then I drop the internet connection (if not the computer) for a while longer than usual, but the address won't change if I hav anything to say about it, and all I hav to say about that is that hiding your e-mail address doesn't work forever, and running (changing) it doesn't work for long.
------------------------------
Message: 5 Date: Fri, 16 Apr 2004 12:03:52 -0500 From: "Paul N. Lee" <Paul.N.Lee@Worldnet.att.net> Subject: [Fractint] Re: FOTD 15-04-04 (Land of Fractals [5]) To: fractint@mailman.xmission.com Cc: philofractal@lists.fractalus.com Message-ID: <408011F8.3C92@Worldnet.att.net> Content-Type: text/plain; charset=us-ascii
James R. McKenzie wrote:
This only rates a "5"?
I too feel that it should have been rated much higher. The unusual images such as these are quite nice to see.
I wish I could run Fractint in XP (Been there tried that, no go) so I could do a 3D transform of the image and see what comes up or "out" as it were. 8-{>
I have seen some Win-XP systems running FractInt produce an image on the monitor that is basically a jumble of pixels. But after it has finished rendering, if the "S" key is pressed to save the image to a directory path, then viewing that image with some graphic editor shows it is not the mess from the screen, and is the correctly formatted fractal graphic.
BTW if anyone does a 1280x1024 of this e-mail me, I'd like a copy.
Try running FractInt at that resolution, then save the image to disk afterwards and see what you get.
Sincerely, P.N.L. ------------------------------------------------- http://home.att.net/~Paul.N.Lee/PNL_Fractals.html http://www.Nahee.com/Fractals/
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Message: 6 Date: Fri, 16 Apr 2004 12:46:33 -0500 From: "Paul N. Lee" <Paul.N.Lee@Worldnet.att.net> Subject: Re: [Fractint] FOTD 16-04-04 (Image of Springtime [5]) To: fractint@mailman.xmission.com Message-ID: <40801BF9.1702@Worldnet.att.net> Content-Type: text/plain; charset=us-ascii
Jim Muth wrote:
FOTD -- April 16, 2004 (Rating 5)
A longer version of today's discussion appears on the philofractal list.
And since I use the postings from the above discussion list for creating Jim's FOTD webpages, then they are also available through the Internet:
<http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
Later, P.N.L. ------------------------------------------------- http://home.att.net/~Paul.N.Lee/PNL_Fractals.html http://www.Nahee.com/Fractals/
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Message: 7 Date: Sat, 17 Apr 2004 09:27:02 -0400 From: Jim Muth <jamth@mindspring.com> Subject: [Fractint] FOTD 17-04-04 (Polyester Minibrot [7]) To: fractint@mailman.xmission.com Cc: philofractal@lists.fractalus.com Message-ID: <1.5.4.16.20040417093023.2c0ff656@pop.mindspring.com> Content-Type: text/plain; charset="us-ascii"
FOTD -- April 17, 2004 (Rating 7)
Fractal visionaries and enthusiasts:
Once again the time has come to enter Fractal Land, that strange land that exists somewhere between the real world around us, which might not be totally real, and the imaginary worlds within us, which might not be totally unreal.
The irregular real(p3) parameter of today's image shows that its parent fractal was found by the Fractint 'evolver' feature. Normally, I round off the odd numbers this feature produces, but for some reason I skipped the rounding process when I started working with today's parent.
The parent fractal is a hugely bloated area of mostly disconnec- ted rings. Today's scene is located near a larger midget that lies in the interior of a ring in the distant north-northeast suburbs of the parent.
The unusual detail inside the midget itself is a sign that the scene has been evaporated, and the ghost brought to life by the bof61 inside fill. Fractals in which all the exponents of Z are negative can be evaporated by raising the escape radius to a full googol, which is the amount entered as the imag(p3) para- meter of today's image. This trick usually traps every point.
For reasons known only to myself and the 'intelligent designer', (whatever you consider this to be), I named the image "Polyester Minibrot". I might have done myself a favor when I rated it at a 7, but the image is really rather pleasant to look at, and I feel it earns its rating. The reasonably fast render time of under 4 minutes gives an overall value of 184.
The render time is fast, but the fastest way of all to enjoy the image is to download it in finished form from the FOTD web site at:
<http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
With a temperature of 67F 19C, gentle breezes, and warm sunshine to keep them happy, the fractal cats put on their best moods Friday. When the day was finished, they were so exhausted that they forgot their customary evening treats, and went right to sleep. Today is starting mostly sunny and warmer. I expect a similar day.
For me, most of the graphics work is caught up. If I can muster the energy this afternoon, I'll give the grass the first trimming of the season. If not, I'll do it tomorrow or Monday. Until next time, take care, and don't get hot under the collar when a cool fractal appears.
Jim Muth jamth@mindspring.com jimmuth@aol.com
START 20.0 PAR-FORMULA FILE================================
Polyester_Minibrot { ; time=0:03:48.11--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+25.24771384422294000/+103.017140882474\ 40000/4599911/1/-22.5/6.18164318095387744e-005 params=2/-1.4/0.2/-8.6/-2.597094637897885/1e+100 float=y maxiter=1200 inside=bof61 periodicity=10 colors=00000U00o00u00x80zOAzdOzuazzozzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzdz0Iz00u50UX02x00zo0Dz00zG0zg0\ U0za0zg0zl0zu0rz0dz0Qz2Gz52zA0zD0zA0z80u50i20_05O0\ AA0G00L00Q00X00a00g00l00g00a00X02U08O0AI0GD0LA0Q50\ X00_00UD0NQ0LgGIoXDzhAsz5zz2zzzzxozodugQo_GiQ2KK00\ Q0ou8_f0zD0zD2zDDzDLgDXODm520a00z00z20z80uD0rI0lL0\ iQ0gX0aa0_g0Ul0Qo0Ou0Ux0_z0az0gz0iz0oz0rz0xz0zz0zz\ 0zz0zz0zz0zz0zz0zz2zzAzzIzuQzi_z_gzOozDxz2zz0zx0zu\ 0zr0zo0zl0zlIzlazluolzglzXlzOlzQozQozUozUozXrzXrz_\ rz_rz_rzdxzizzlzzrzzuzzzzzzzzuzzlzzgzz_zzUzzGzz5zz\ 0lz0Xa_dAzi5zl0zl0zo0zo0zr0zr0xu0uu0ox0lx0iz0gz0dz\ 0iz0oz0rz0xz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0z\ z0zz0zz0ro0da0UL2G822050080080000000000000A00O02a0\ 8r0Dz0Iz0Oz0UiG_QadAxi0zo0zu0za0zI5x2Qi0lX0zI0z800\ 00I0Gz0Gz0Gz0Gz0Gz0Gz0Gz0Gz0Gz0Lu0Oo0Ql0Ug0Xa0__0a\ U0dQ0gL0iG0lD0o80O0080008 }
frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l }
END 20.0 PAR-FORMULA FILE==================================
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End of Fractint Digest, Vol 14, Issue 7 ***************************************